1. Field of the Invention
The invention is in the field of dual resonant transformers used for charging pulse-forming networks, and in particular relates to a design for the improved efficiency for such transformers.
2. Description of the Prior Art
The dual resonant transformer is important in applications requiring the charging of Pulse Forming Networks (PFN) because it provides a high voltage step-up, has a high energy transfer efficiency, and is very compact and inherently well configured for megavolt level operation. The simplified circuit of a dual resonant transformer applied to a PFN charging circuit is shown in FIG. 1. The operation consists of initially storing energy in the primary capacitor, C1, at a low voltage, typically on the order of 50 kV. The PFN, or other capacitive load to be charged, is connected to the secondary of the transformer. The total secondary equivalent capacitance, C2, consists of the PFN (or other load) capacitance, CPFN, plus the stray capacitance, Cs. The primary open-circuit inductance of the transformer is L1, and the secondary open-circuit inductance is L2. The double tuned condition is implemented by satisfying the relation, L1*C1=L2*C2. The voltage ratio, that is the voltage to which C2 (PFN and stray capacitance) is to be charged, divided by the initial voltage on C1, is determined by the square-root of the inductance ratio, (L2/L1)xc2xd. In addition to both of these conditions the coupling coefficient of the transformer must be 0.600. That is k=M12/(L1*L2)xc2xd, where M12, is the mutual inductance between L1 and L2.
When all three of these conditions are fulfilled the initial energy in C1 will be totally transferred to C2 in a time duration of 1.6673*(L1*C1)xc2xd=1.6673*(L2*C2)xc2xd, measured from the closure of the switch connecting C1 to the primary of the transformer. The capacitance C2 is the total effective capacitance on the secondary of the transformer and consists of the useful load capacitance and the transformer xe2x80x9cstrayxe2x80x9d capacitance. The normalized voltage waveforms of V1 and V2 are also shown in FIG. 1. It is important to recognize that a high-energy transfer efficiency does not necessarily mean a high over-all efficiency. In applications where the useful load capacitance is on the order of, or less than, the stray capacitance, the loss of the stray capacitance energy greatly limits the efficiency of the transformer charging system. Such applications include Ultra Wide Band (UWB) generators. In UWB applications the pulse being generated typically has a voltage amplitude on the order of a megavolt and is of nanosecond or sub-nanosecond duration. Consequently the pulse has a very low energy content, typically on the order of a few joules. At megavolt operating voltages the electric field stress must be carefully managed to prevent arc down faults in the insulation. To accomplish this it is necessary to use field shaping conductors to eliminate high stress concentrations related to geometry features with small radii of curvature.
The effect of shielding is illustrated in FIGS. 2a and 2b, both of which show a cross-section of a cylindrical coil. The ground end of the coil is to the outside and the high voltage end is to the inside. The equipotential field lines have been calculated using a computerized Laplace solver. The intensity of the electric field is indicated by the closeness or bunching of the equipotential lines. It can be seen that with xe2x80x9cdoughnutxe2x80x9d ring shield 11, the bunching is reduced and thus the electric field stress is lower. The introduction of ring shield 11 increases the stray capacitance of the system and also couples to the magnetic field of the transformer. The stray capacitance increases the energy storage.
It is the purpose of the present invention to make productive use of this increased energy storage. The coupling to the magnetic field reduces the transformer inductances and also decreases the coupling coefficient. These magnetic effects can be completely counteracted by carefull design of the field shaping conductors or shields in relation to the magnetic field of the transformer. At a voltage of 1 MV, a capacitance of 1 pF corresponds to an energy of xc2xd Joule. A typical transformer stray capacitance is on the order of 50 pF or 25 Joules at 1 MV, therefore, the degradation of efficiency is very significant for UWB or other low pulse energy applications.
FIGS. 3a and 3b show, in more detail, typical xe2x80x9cdoughnutxe2x80x9d ring shields 11. The shields 11 must have a gap 13 to prevent the ring from acting as a shorted turn on the transformer flux. The ring shields 11 must also be connected electrically by lead 15 to the output connection electrode or lead in order to accomplish the field grading function. The very nature of the rings as well as the electrical connections are inductive. Therefore, because of this inductance, the capacitive energy stored in the ring cannot be rapidly removed to the load. A simplified equivalent circuit illustrating this is shown in FIG. 4.
The equivalent circuit in FIG. 4 shows how the capacitive energy stored in the grading rings and the transformer secondary winding must pass through the inductance of the rings and the electrical connections to be delivered to the output. In so doing, this energy is delayed by the inductance and is therefore not available as useful output energy on a fast time scale.
High voltage cylindrical air core transformers must have shields to control the electric field stress. However, the energy stored in conventional shields cannot be usefully extracted. The present invention provides for this shield by means of a new coaxial type configuration. Slots in the shield permit the normal transformer flux to couple the primary and secondary windings. This coaxial shield provides the required electric field stress control as well as the conventional shield does. In addition, the coaxial shield permits the very rapid extraction of the energy stored in the electric field, which then becomes useful output energy. The energy stored in the coaxial shield is approximately equal to that which would be stored in a conventional shield having a capacitance of typically 50 picoFarads. In applications such as UWB, the total load capacitance is also on the order of 50 picoFarads, leading to a factor of two improvement in efficiency.